Solve 4p^3*5p^-4

$$4 p ^ { 3 } \times 5 p ^ { - 4 }$$

Evaluate

$$\frac{20}{p}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and -4 to get -1.

$$4p^{-1}\times 5$$

Multiply 4 and 5 to get 20.

$$20p^{-1}$$

Differentiate w.r.t. p

$$-\frac{20}{p^{2}}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 3 and -4 to get -1.

$$\frac{\mathrm{d}}{\mathrm{d}p}(4p^{-1}\times 5)$$

Multiply 4 and 5 to get 20.

$$\frac{\mathrm{d}}{\mathrm{d}p}(20p^{-1})$$

The derivative of ax^{n} is nax^{n-1}.

$$-20p^{-1-1}$$

Subtract 1 from -1.

$$-20p^{-2}$$